After the Supreme Court decided the case of Missouri v. McNeely, the question of when a warrant is required, before law enforcement may draw a person's blood became more interesting to say the least. On one side of the issue was the position that a blood alcohol concentrations is constantly changing, thus, there is a justification for law enforcement to bypass the traditional warrant requirement.
The contrary, and as it turns out the prevailing position, is that our Constitution does not allow law enforcement unfettered discretion to decided if they can stick a needle in your arm without a warrant (i.e. probable cause presented to a judge who issues a warrant). The reality of modern technology is that a telephonic warrant can be obtained in about 15 minutes for most cases. Accordingly, the exigent circumstances reasoning for bypassing the warrant requirement is unsound. As the U.S. Supreme Court stated in their rejection of such a per se rule in DUI cases:
But it does not follow that we should depart from careful case-by-case assessment of exigency and adopt the categorical rule proposed by the State and its amici. In those drunk-driving investigations where police officers can reasonably obtain a warrant before a blood sample can be drawn without significantly undermining the efficacy of the search, the Fourth Amendment mandates that they do so. See McDonald v. United States, 335 U.S. 451, 456, 69 S.Ct. 191, 93 L.Ed 153 (1948).
Missouri v. McNeely, 133 S.Ct. at 1555 (2013).